Maximize distance between variables' value in SWI-Prolog(clpfd)

clpfd, constraint-programming, prolog, swi-prolog

Solution

There is no constraint to express maximum difference. Nor any constraint to express a maximum1. To permit such a construct some form of quantification would be necessary. And/or problems with monotonicity would arise.

However, there is something related: you might want to generate values such that the largest value is produced first:

:- use_module(library(clpfd)).
maximize(Xs) :- 
    Xs = [A,B],
    Xs ins 1..5,
    labeling([max(abs(A-B))],Xs).

?- maximize(Xs).
   Xs = [1,5]
;  Xs = [5,1]
;  Xs = [1,4]
;  Xs = [2,5]
;  Xs = [4,1]
; ... .

So it starts with the biggest distance and then lowers it one-by one.

At first this behavior might surprise you, but recall what the manual states

Labeling is always complete, always terminates, and yields no redundant solutions.

This is a very strong guarantee!

If you now want just the first solution, wrap a `once/1` around `labeling/2` but keep in mind that you then left the realm of pure, monotonic programs.

Footnote 1: It is possible to express the maximum of two variables `max(X,Y)` but this does not constrain the maximum to be the largest possible value! It will be only the largest value of `X` and `Y`.

Problem

I want to maximize the difference between two variables: ``` :- use_module(library(clpfd)). maximize(X) :- X = [A,B], X ins 1..5, % I want to write a constraint to have maximum difference between A and B. ```

Original source